Likely an editing error, but...
I agree with Thomas Markov's answer that this is likely a design oversight and failure of the editors to catch. I even agree with his comment that the amulet as written does not provide a specific-over-general exception to using a bonus action.
Whether a mistake or not, it is easy to excuse the error - Chains of Asmodeus is a charity product, and may not have had the same standards of editing as a product released for profit. And the stunned condition itself does not say it prohibits bonus actions - this is hidden behind a chain of unlisted rules. First you have to realize that since being stunned imposes the incapacitated condition, and being incapacitated means you can't take actions. Then you have to remember that "anything that deprives you of your ability to take actions also prevents you from taking a bonus action."
So, again, it seems like a reasonable assumption that this was a mistake. However, for the sake of completeness, we can ask whether there is ever a time you would be able to use the amulet as written.
To do so, you would need to have the stunned condition, but not be affected by it so that you could use your bonus action to pass it along. Note that the amulet says it does not work if your target is immune to stun, but places no such restriction on you. So how could you be immune to stun, but have a latent stunned condition to pass on with your bonus action?
One possibility is if you started a round both stunned and attuned to the amulet, with the amulet nearby but not actually wearing it1. On their turn, an ally of yours then cast true polymorph on you, turning you into a creature that was immune to stun. There are many of these, but we can immediately exclude swarms, those with a CR of more than 20, and those whose anatomy precludes them using an amulet (many of the creatures on this list are some variation of a floating skull). Including a few who are unique individuals, that's still 25+ options. Then on your turn, you will not be stunned (because you are immune) even though you have the stunned condition. Since you are not stunned, you can free object interaction don the amulet, then use the bonus action granted by the amulet to pass on your stunned condition to an ally.
We know that when you are made immune, your stunned condition does not 'drop off', but rather becomes "suppressed" because of a Sage Advice Compendium ruling:
If the heroism spell is cast on a character that is already frightened, does it remove the frightened effect?
The heroism spell would suppress a frightening effect that was already on its target. When the spell ends, the target’s immunity goes away and the frightening effect resumes if it has not expired or been removed.
The above SAC ruling makes it clear that if you are already stunned and then become immune, the stun condition is merely suppressed, and is available for transfer via the amulet. A more difficult question is what happens if you are already immune to stun while you are wearing the amulet. If an effect would impose the stunned condition on you, but you are immune, does the effect simply fail, or does it take hold but only as a suppressed effect?
Unfortunately there is not an official answer or ruling here, as far as I can tell. This site seems to favor the ruling of 'current immunity makes you ineligible as a target of the effect'. That is the logic of the accepted answer of Is an Immune creature considered to have the condition without suffering its effects? and is what is argued by the most-upvoted answer to What happens when exhaustion passes 6th level on an immune creature? Still, there is not an official ruling on this, so you might be playing with a DM who rules that if you are immune at the time of targeting, you gain the stunned condition but it is suppressed, and you might later become stunned if you lose immunity.
If this is how your DM rules, then you could have been true-polymorphed into a form that is immune to stun and be wearing the amulet when the stun effect landed. Or, you could have another source of immunity. As an even edgier edge case, for example, you might be playing a Path of the Juggernaut Barbarian2 whose level 14 Unstoppable ability gives immunity to the Stunned condition while raging.
1 You can't actually be wearing the amulet when you are transformed, since the true polymorph spell says: "The target’s gear melds into the new form. The creature can’t activate, use, wield, or otherwise benefit from any of its equipment."
2 Based on the Critical Role campaign, the Tal'Dorei campaign and Path of the Juggernaut Barbarian is not official 5e content.